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I work in Combinatorial Optimization.
My main research interest is Matroid Theory.
With Jim Geelen and
Geoff Whittle,
I work on generalizing Robertson and Seymour's Graph Minor Theory to matroids representable over any fixed finite field.
Our targets are the conjectures by Robertson and Seymour that such matroids are well-quasi-ordered
by minors and can be tested in polynomial time for having a specific minor, and
Rota's conjecture that such representability can be characterized by finitely many excluded minors.
Challenge and bulk of the work is to understand the structure of minor-closed classes of the matroids over the specific field.
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Publications
(click on item for pdf)
Characterizing graphic matroids by a system of linear equations
- with J. Geelen (submitted)
On inequivalent representations of matroids over non-prime fields
- with J. Geelen and G. Whittle
Tangles, tree-decompositions, and grids in matroids
- with J. Geelen and G. Whittle
Excluding a group-labelled graph
- with J. Geelen
On the odd-minor variant of Hadwicher's conjecture
- with J. Geelen, B. Reed, P. Seymour and A. Vetta
Packing odd circuits
- with M. Conforti
Excluding a planar graph from GF(q)-representable matroids
- with J. Geelen and G. Whittle
Mixed-integer vertex covers on bipartite graphs
- with M. Conforti and G. Zambelli
Packing non-zero A-paths in group-labeled graphs
- with M. Chudnovski, J. Geelen, L. Goddyn, M. Lohman and P. Seymour
Obstructions to branch-decomposition of matroids
- with J. Geelen, N. Robertson and G. Whittle
Matroid T-connectivity
- with J. Geelen and G. Whittle
On Rota's Conjecture and excluded minors containing large projective geometries
- with J. Geelen and G. Whittle
Regular matroid decomposition via signed graphs
- with J. Geelen
On the excluded minors for the matroids of branch-width k
- with J. Geelen, N. Robertson and G. Whittle
Disjoint cocircuits in matroids with large rank
- with J. Geelen and G. Whittle
Note on: N.E. Aguilera, M.S. Escalante, G.L. Nasini, "A Generalization of the Perfect Graph Theorem under the Disjunctive Index"
- with G. Mároti and A. Schrijver
Branch width and well-quasi-ordering in matroids and graphs
- with J. Geelen and G. Whittle
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The excluded minors for GF(4)-representable matroids
- with J. Geelen and A. Kapoor
A theorem of Truemper
- with M. Conforti and A. Kapoor
Strong orientations without even directed circuits
- with F.B. Shepherd
The graphs with all subgraphs t-perfect
- with F.B. Shepherd
On Tutte's characterization of graphic matroids - a graphic proof.
A characterization of box 1/d-integral binary clutters
- with M. Laurent
An orientation theorem for graphs
On shortest T-joins and packing T-cuts
Compact systems for T-join and perfect matching polyhedra of graphs with bounded genus
On matrices and cutting planes
A short proof of Tutte's characterization of totally unimodular matrices
An extension of König's theorem to graphs with no odd-K4
Homomorphisms of graphs into odd circuits
Total dual integrality implies local strong unimodularity
- with A. Sebö
Matrices with the Edmonds-Johnson property
- with A. Schrijver
Sensitivity theorems in integer linear programming
- with W. Cook, A. Schrijver and É. Tardos
Testing the odd bicycle wheel inequalities for the bipartite subgraph polytope
Spectral localization in Banach algebras
- with S. Ackermans
Survey articles, monograph, etc.
Towards a matroid-minor structure theory
- with J. Geelen and G. Whittle
Towards a structure theory for matrices and matroids
- with J. Geelen and G. Whittle
Matching
Multicommodity flows and polyhedra
Graphs and polyhedra - Binary spaces and cutting planes
Polyhedral combinatorics in combinatorial optimization
- with A. Kolen
Edited
Eighth MPS Conference on Integer Programming and Combinatorial Optimization
- with K. Aardal
Unpublished
On 2-vertex connected orientations
Odd paths and circuits in planar graphs with two odd faces
Onion skins in oriented matroids
- with W. Hochstättler
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